Welcome to the community!
Without getting into how you got your music, yes, you can download your songs on to your phone. You can either load the music files on a micro-SD card (most newer Samsungs support them) or you can download them to your phone. This webpage provides information on how to load music files from a Windows PC. One possible limitation, however, is that the amount of music you can load on to your phone depends on its available storage.
Depending on the age of your Samsung phone, the stock music player should be able to play most music files (ie MP3). There are also other media player apps available.
Hope this helps 😀